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2019 | OriginalPaper | Buchkapitel

Optimal Gathering by Asynchronous Oblivious Robots in Hypercubes

verfasst von : Kaustav Bose, Manash Kumar Kundu, Ranendu Adhikary, Buddhadeb Sau

Erschienen in: Algorithms for Sensor Systems

Verlag: Springer International Publishing

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Abstract

We consider the problem of gathering a set of autonomous, identical, oblivious, asynchronous, mobile robots at a vertex of an anonymous hypercube. The robots operate in Look-Compute-Move cycles. In each cycle, a robot takes a snapshot of the current configuration (Look), then based on the perceived configuration, decides whether to stay idle or to move to an adjacent vertex (Compute), and in the later case makes an instantaneous move accordingly (Move). We have shown that the problem is unsolvable if the robots do not have multiplicity detection capability. With weak multiplicity detection capability, the problem is solvable in an oriented hypercube for any initial configuration of \(2k+1 (k > 0)\) number of robots. For \(4k (k > 0)\) number of robots, the problem is solvable under the same assumptions if and only if the group of automorphism of the configuration is trivial. Our proposed algorithms are optimal with respect to the total number of moves executed by the robots.

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Vorheriges Kapitel Mutual Visibility by Asynchronous Robots on Infinite Grid

Nächstes Kapitel Barrier Coverage Problem in 2D

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Titel: Optimal Gathering by Asynchronous Oblivious Robots in Hypercubes
verfasst von: Kaustav Bose
Manash Kumar Kundu
Ranendu Adhikary
Buddhadeb Sau
Verlag: Springer International Publishing
Buch: Algorithms for Sensor Systems
Print ISBN: 978-3-030-14093-9

Electronic ISBN: 978-3-030-14094-6

Copyright-Jahr: 2019
DOI: https://doi.org/10.1007/978-3-030-14094-6_7

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